[petsc-users] using petsc tools to solve isolated irregular domains with finite difference

Bishesh Khanal bisheshkh at gmail.com
Mon Oct 28 10:13:40 CDT 2013 

On Mon, Oct 28, 2013 at 3:49 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Oct 28, 2013 at 9:06 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>
>>
>> On Mon, Oct 28, 2013 at 1:40 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>
>>> On Mon, Oct 28, 2013 at 5:30 AM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>
>>>>
>>>>
>>>>
>>>> On Fri, Oct 25, 2013 at 10:21 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>>
>>>>> On Fri, Oct 25, 2013 at 2:55 PM, Bishesh Khanal <bisheshkh at gmail.com>wrote:
>>>>>
>>>>>> On Fri, Oct 25, 2013 at 8:18 PM, Matthew Knepley <knepley at gmail.com>wrote:
>>>>>>
>>>>>>> On Fri, Oct 25, 2013 at 12:09 PM, Bishesh Khanal <
>>>>>>> bisheshkh at gmail.com> wrote:
>>>>>>>
>>>>>>>> Dear all,
>>>>>>>> I would like to know if some of the petsc objects that I have not
>>>>>>>> used so far (IS, DMPlex, PetscSection) could be useful in the following
>>>>>>>> case (of irregular domains):
>>>>>>>>
>>>>>>>> Let's say that I have a 3D binary image (a cube).
>>>>>>>> The binary information of the image partitions the cube into a
>>>>>>>> computational domain and non-computational domain.
>>>>>>>> I must solve a pde (say a Poisson equation) only on the
>>>>>>>> computational domains (e.g: two isolated spheres within the cube). I'm
>>>>>>>> using finite difference and say a dirichlet boundary condition
>>>>>>>>
>>>>>>>> I know that I can create a dmda that will let me access the
>>>>>>>> information from this 3D binary image, get all the coefficients, rhs values
>>>>>>>> etc using the natural indexing (i,j,k).
>>>>>>>>
>>>>>>>> Now, I would like to create a matrix corresponding to the laplace
>>>>>>>> operator (e.g. with standard 7 pt. stencil), and the corresponding RHS that
>>>>>>>> takes care of the dirchlet values too.
>>>>>>>> But in this matrix it should have the rows corresponding to the
>>>>>>>> nodes only on the computational domain. It would be nice if I can easily
>>>>>>>> (using (i,j,k) indexing) put on the rhs dirichlet values corresponding to
>>>>>>>> the boundary points.
>>>>>>>> Then, once the system is solved, put the values of the solution
>>>>>>>> back to the corresponding positions in the binary image.
>>>>>>>> Later, I might have to extend this for the staggered grid case too.
>>>>>>>> So is petscsection or dmplex suitable for this so that I can set up
>>>>>>>> the matrix with something like DMCreateMatrix ? Or what would you suggest
>>>>>>>> as a suitable approach to this problem ?
>>>>>>>>
>>>>>>>> I have looked at the manual and that led me to search for a simpler
>>>>>>>> examples in petsc src directories. But most of the ones I encountered are
>>>>>>>> with FEM (and I'm not familiar at all with FEM, so these examples serve
>>>>>>>> more as a distraction with FEM jargon!)
>>>>>>>>
>>>>>>>
>>>>>>> It sounds like the right solution for this is to use PetscSection on
>>>>>>> top of DMDA. I am working on this, but it is really
>>>>>>> alpha code. If you feel comfortable with that level of development,
>>>>>>> we can help you.
>>>>>>>
>>>>>>
>>>>>> Thanks, with the (short) experience of using Petsc so far and being
>>>>>> familiar with the awesomeness (quick and helpful replies) of this mailing
>>>>>> list, I would like to give it a try. Please give me some pointers to get
>>>>>> going for the example case I mentioned above. A simple example of using
>>>>>> PetscSection along with DMDA for finite volume (No FEM) would be great I
>>>>>> think.
>>>>>> Just a note: I'm currently using the petsc3.4.3 and have not used the
>>>>>> development version before.
>>>>>>
>>>>>
>>>>> Okay,
>>>>>
>>>>> 1)  clone the repository using Git and build the 'next' branch.
>>>>>
>>>>> 2) then we will need to create a PetscSection that puts unknowns where
>>>>> you want them
>>>>>
>>>>> 3) Setup the solver as usual
>>>>>
>>>>> You can do 1) an 3) before we do 2).
>>>>>
>>>>> I've done 1) and 3). I have one .cxx file that solves the system using
>>>> DMDA (putting identity into the rows corresponding to the cells that are
>>>> not used).
>>>> Please let me know what I should do now.
>>>>
>>>
>>> Okay, now write a loop to setup the PetscSection. I have the DMDA
>>> partitioning cells, so you would have
>>> unknowns in cells. The code should look like this:
>>>
>>> PetscSectionCreate(comm, &s);
>>> DMDAGetNumCells(dm, NULL, NULL, NULL, &nC);
>>> PetscSectionSetChart(s, 0, nC);
>>> for (k = zs; k < zs+zm; ++k) {
>>>   for (j = ys; j < ys+ym; ++j) {
>>>     for (i = xs; i < xs+xm; ++i) {
>>>       PetscInt point;
>>>
>>>       DMDAGetCellPoint(dm, i, j, k, &point);
>>>       PetscSectionSetDof(s, point, dof); // You know how many dof are on
>>> each vertex
>>>     }
>>>   }
>>> }
>>> PetscSectionSetUp(s);
>>> DMSetDefaultSection(dm, s);
>>> PetscSectionDestroy(&s);
>>>
>>> I will merge the necessary stuff into 'next' to make this work.
>>>
>>
>> I have put an example without the PetscSection here:
>> https://github.com/bishesh/petscPoissonIrregular/blob/master/poissonIrregular.cxx
>> From the code you have written above, how do we let PetscSection select
>> only those cells that lie in the computational domain ?  Is it that for
>> every "point" inside the above loop, we check whether it lies in the domain
>> or not, e.g using the function isPosInDomain(...) in the .cxx file I linked
>> to?
>>
>
> 1) Give me permission to comment on the source (I am 'knepley')
>
> 2) You mask out the (i,j,k) that you do not want in that loop
>

Done.
I mask it out using isPosInDomain() function::
       if(isPosInDomain(&testPoisson,i,j,k)) {
            ierr = DMDAGetCellPoint(dm, i, j, k, &point);CHKERRQ(ierr);
            ierr = PetscSectionSetDof(s, point, testPoisson.mDof); // You
know how many dof are on each vertex
          }

And please let me know when I can rebuild the 'next' branch of petsc so
that DMDAGetCellPoint can be used. Currently compiler complains as it
cannot find it.

>
>    Matt
>
>
>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>>
>>>>>  If not, just put the identity into
>>>>>>> the rows you do not use on the full cube. It will not hurt
>>>>>>> scalability or convergence.
>>>>>>>
>>>>>>
>>>>>> In the case of Poisson with Dirichlet condition this might be the
>>>>>> case. But is it always true that having identity rows in the system matrix
>>>>>> will not hurt convergence ? I thought otherwise for the following reasons:
>>>>>> 1)  Having read Jed's answer here :
>>>>>> http://scicomp.stackexchange.com/questions/3426/why-is-pinning-a-point-to-remove-a-null-space-bad/3427#3427
>>>>>>
>>>>>
>>>>> Jed is talking about a constraint on a the pressure at a point. This
>>>>> is just decoupling these unknowns from the rest
>>>>> of the problem.
>>>>>
>>>>>
>>>>>> 2) Some observation I am getting (but I am still doing more
>>>>>> experiments to confirm) while solving my staggered-grid 3D stokes flow with
>>>>>> schur complement and using -pc_type gamg for A00 matrix. Putting the
>>>>>> identity rows for dirichlet boundaries and for ghost cells seemed to have
>>>>>> effects on its convergence. I'm hoping once I know how to use PetscSection,
>>>>>> I can get rid of using ghost cells method for the staggered grid and get
>>>>>> rid of the identity rows too.
>>>>>>
>>>>>
>>>>> It can change the exact iteration, but it does not make the matrix
>>>>> conditioning worse.
>>>>>
>>>>>    Matt
>>>>>
>>>>>
>>>>>>  Anyway please provide me with some pointers so that I can start
>>>>>> trying with petscsection on top of a dmda, in the beginning for
>>>>>> non-staggered case.
>>>>>>
>>>>>> Thanks,
>>>>>> Bishesh
>>>>>>
>>>>>>>
>>>>>>>   Matt
>>>>>>>
>>>>>>>
>>>>>>>> Thanks,
>>>>>>>> Bishesh
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> What most experimenters take for granted before they begin their
>>>>>>> experiments is infinitely more interesting than any results to which their
>>>>>>> experiments lead.
>>>>>>> -- Norbert Wiener
>>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>>
>>>>> --
>>>>> What most experimenters take for granted before they begin their
>>>>> experiments is infinitely more interesting than any results to which their
>>>>> experiments lead.
>>>>> -- Norbert Wiener
>>>>>
>>>>
>>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>
>>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
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